I just asked this question on another site but with only a handful of somewhat helpful responses.
I just made the following integral problem which I think is very cool and nice, but I don't know how to solve it. (I found it by taking the derivative which is what you see here.)
$\int \left(\frac{x^2-2}{x^3+6x} \right)^2 dx$. (I won't tell you the answer.)
Once I had obtained this nice looking derivative and turned it into a nice looking integration problem I wanted to make more such problems, but the functions I was deriving didn't really seem to have challenging nor interesting derivatives.
How can I come up with some fun integration problems (definite or indefinite)? I should also mention that my knowledge of calculus does not include complex analysis such as the Residues things or the contour theorems, only basic Calc 2 level stuff (eg. taylor series, integration by parts, integration tables from my physics textbook as I don't know where my calculus one is.)
